A246636 - OEIS

%I #12 Nov 30 2023 01:26:26

%S 0,1,5,17,41,125,161,377,485,881,1457,2645,3077,3941,5417,9197,11825,

%T 14405,16757,18521,24965,26405,37337,39365,42461,71441,77657,95921,

%U 99077,113777,117305,143261,174761,175445,184841,265481,304037,308825,318401,351917

%N Numbers k such that C(k+2,2) divides 2^(k+1) - 1.

%C These are the numbers k such that mean of the numbers in the first k rows of Pascal' s triangle is an integer.  All such k except 1 are congruent to -1 mod 6.

%H Robert Israel, <a href="/A246636/b246636.txt">Table of n, a(n) for n = 1..181</a>

%e The sum of the numbers in Pascal's triangle, from row 0 through row 17, is 2^18 - 1 = 262143; the number of such numbers is C(19,2) = 171, and 262143/171 = 1533; thus 17 is in this sequence, and 1533 is in A246637.

%p select(k -> 2 &^(k+1) - 1 mod ((k+1)*(k+2)/2) = 0, [$0..10^6]); # _Robert Israel_, Nov 30 2023

%t z = 1000;

%t t = Select[Range[0, z], IntegerQ[(2^(# + 1) - 1)/Binomial[# + 2, 2]] &]

%Y Cf. A246637, A007318.

%K nonn,easy

%O 1,3

%A _Clark Kimberling_, Sep 01 2014

%E Offset corrected by _Robert Israel_, Nov 30 2023